Question 3 John takes up a $1 million housing loan from a bank. The loan is to be amortized over 15 years with monthly repayments made at the end of each month, calculated based on a nominal annual loan interest rate of 4%, with monthly compounding. The term of the loan is provided that, at any time after 3 years, the bank could alter the loan interest rate, in which case the amount of subsequent monthly repayments would be revised accordingly. (a) Find the initial amount of the loan repayment to be made by John at the end of each month. (5 marks) Question 3 (continued) (b) Immediately after the 57th payment, the bank increases the loan interest rate to 5%. Find the revised monthly repayment amount to be made by John. (7 marks) (c) Immediately after the last payment is made at the end of 10 years, the bank increases the annual loan interest rate to 6%, and there is no further change in the loan interest rate for the remaining 5 years of the loan. Calculate the total dollar interest paid by John over the entire15-year loan period. (10 marks)